Marquette University e-Publications@Marquette Master's Theses (2009 -) Dissertations, Theses, and Professional Projects Performance Analysis of Constant Speed Local Abstacle Avoidance Controller Using a MPC Algorithym on Granular Terrain Nicholas Haraus Marquette University Recommended Citation Haraus, Nicholas, "Performance Analysis of Constant Speed Local Abstacle Avoidance Controller Using a MPC Algorithym on Granular Terrain" (2017). Master's Theses (2009 -). 443. http://epublications.marquette.edu/theses_open/443 PERFORMANCE ANALYSIS OF A CONSTANT SPEED LOCAL OBSTACLE AVOIDANCE CONTROLLER USING A MPC ALGORITHM ON GRANULAR TERRAIN by Nicholas Haraus, B.S.M.E. A Thesis submitted to the Faculty of the Graduate School, Marquette University, in Partial Fulfillment of the Requirements for the Degree of Master of Science Milwaukee, Wisconsin December 2017 ABSTRACT PERFORMANCE ANALYSIS OF A CONSTANT SPEED LOCAL OBSTACLE AVOIDANCE CONTROLLER USING A MPC ALGORITHM ON GRANULAR TERRAIN Nicholas Haraus, B.S.M.E. Marquette University, 2017 A Model Predictive Control (MPC) LIDAR-based constant speed local obstacle avoidance algorithm has been implemented on rigid terrain and granular terrain in Chrono to examine the robustness of this control method. Provided LIDAR data as well as a target location, a vehicle can route itself around obstacles as it encounters them and arrive at an end goal via an optimal route. This research is one important step towards eventual implementation of autonomous vehicles capable of navigating on all terrains. Using Chrono, a multibody physics API, this controller has been tested on a complex multibody physics HMMWV model representing the plant in this study. A penalty-based DEM approach is used to model contacts on both rigid ground and granular terrain. Conclusions are drawn regarding the MPC algorithm performance based on its ability to navigate the Chrono HMMWV on rigid and granular terrain. A novel simulation framework has been developed to efficiently simulate granular terrain for this application. Two experiments were conducted to analyze the performance of the MPC LIDAR-based constant speed local obstacle avoidance controller. In the first, two separate controllers were developed, one using a 2-DOF analytical model to predict the HMMWV behavior, and the second using a higher fidelity 14-DOF vehicle model. In this first experiment, two controllers were compared as they controlled the HMMWV on two obstacle fields on rigid ground and granular terrain to understand the influence of model fidelity and terrain on controller performance. From these results, an improved lateral force model was developed for use in the 2-DOF vehicle model to better model the tire ground interaction using terramechanics relations. A second experiment was performed to compare two developed controllers. One used the 2-DOF vehicle model using the Pacejka Magic Formula to estimate tire forces while the second used a 2-DOF vehicle model with the newly developed force model to estimate lateral tire forces. As a result of this research, a smarter controller was developed that uses friction angle, cohesion, and interparticle friction coefficient to more accurately predict vehicle trajectories on granular terrain and allow a vehicle to navigate autonomously on granular terrain. i ACKNOWLEDGEMENTS Nicholas Haraus, B.S.M.E. Obtaining a degree has not been a solo pursuit, and therefore I would like to express my deep appreciation and gratitude in no particular order to: My loving family, for their continued support of me throughout my life and educational journey. Sara, for her love, care, support, humor, and encouragement to continue pushing forward even in the most stressful times. My close friends, for the distractions and adventures that made my time at Marquette all the more memorable. My adviser, Dr. Jonathan Fleischmann, for the opportunity to work with him for the past few years, enabling me to grow as a student, researcher, engineer, and person. Dr. Philip Voglewede, for the technical expertise, advice, and for teaching me...and reteaching me...and reteaching me....that spring mass damper systems are in fact everywhere. All the faculty and staff at Marquette for providing an incredible educational experience. Dr. Radu Serban and Dr. Dan Negrut from the Simulation Based Engineering Laboratory in Madison, for their support and collaboration throughout this research endeavor. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS i LIST OF TABLES iv LIST OF FIGURES v 1 INTRODUCTION 1 1.1 Problem Summary . 2 1.2 Literature Review . 4 1.2.1 Early Obstacle Avoidance Algorithms: Artificial Potential Field, Vector Field Histogram, and Dynamic Window Approaches . 4 1.2.2 MPC Algorithms . 11 1.2.3 MPC Algorithms for Car-Like Vehicle . 14 1.2.4 Extending Rigid Ground Tests to Granular Terrain . 17 1.2.5 Simulating Granular Terrain for Vehicular Applications . 18 1.2.6 Summary . 20 1.3 Objectives and Methodology . 20 2 THEORETICAL BACKGROUND 23 2.1 Multibody Dynamics Background . 23 2.2 Dealing with Contacts: The Penalty Method . 25 2.3 Chrono Multibody Physics Package . 28 2.3.1 Vehicle Modeling . 28 2.4 MPC LIDAR-Based Local Obstacle Avoidance: History and Current Algorithm . 29 2.5 Multi-DOF Vehicle Dynamics Models . 34 2.5.1 2-DOF Vehicle Model . 35 2.5.2 14-DOF Vehicle Model . 36 iii 2.6 Tire Ground Force Model: Pacejka Magic Formula . 37 2.7 Optimization Problem: Exhaustive Search Space . 39 3 EXPERIMENTAL SETUP 43 3.1 Controlled Chrono HMMWV Vehicle . 43 3.2 Simulation Parameters . 45 3.3 Evaluation Metrics . 47 3.4 Granular Terrain Simulation . 47 3.5 Hardware and Materials . 54 4 FIRST EXPERIMENTAL RESULTS AND DISCUSSION 56 4.1 Influence of Model Fidelity . 57 4.2 Influence of Terrain Type . 58 5 IMPROVED VEHICLE MODEL ON GRANULAR MATERIAL 61 5.1 Bekker/Wong Load Sinkage Relationship . 62 5.2 New Simplified Force Model . 63 5.3 Open Loop Comparisons . 66 6 SECOND EXPERIMENTAL RESULTS TO TEST IMPROVED VEHICLE MODEL 70 6.1 Experimental Setup . 70 6.2 Results . 71 7 CONCLUSIONS 75 7.1 Future Work . 80 BIBLIOGRAPHY 84 APPENDIX A: RAY-CIRCLE INTERSECTION ALGORITHM 88 APPENDIX B: POINT IN POLYGON ALGORITHM 91 iv LIST OF TABLES 3.1 Individual Simulation Test Information . 45 3.2 Obstacle Field Parameters . 46 3.3 Hardware Components of Computer Used for Parallel Simulations . 55 4.1 Experiment 1 Test Evaluation Metrics Summary on Obstacle Field 1 56 4.2 Experiment 1 Test Evaluation Metrics Summary on Obstacle Field 2 57 6.1 Compared Simulations for Second Experiment . 70 6.2 Experiment 2 Test Evaluation Metrics Summary on Obstacle Field 1 71 6.3 Experiment 2 Test Evaluation Metrics Summary on Obstacle Field 2 72 v LIST OF FIGURES 1.1 Comparison from Literature Review of Artificial Potential Field, Vector Field Histogram, and Dynamic Window Approaches to local obstacle avoid- ance .................................... 10 2.1 Reproduced from [1]. DEM-P contact model with normal overlap distance δn, contact-normal unit vector n, and tangential displacement vector ut (top), and a Hookean-linear contact force-displacement model with constant Coulomb sliding friction (bottom) ..................... 26 2.2 Schematic of MPC LIDAR-Based Constant Speed Local Obstacle Avoidance Controller ................................. 30 2.3 Sample obstacle field and LIDAR output . 31 2.4 2-DOF Vehicle Model ........................... 36 2.5 Reproduced from [2]. 14-DOF Vehicle Model . 37 2.6 Exhaustive Search Space Simplified Visualization . 40 2.7 Exhaustive Search Space Paths Checked with Point in Polygon Algorithm 41 3.1 Full-vehicle HMMWV multibody model. 44 3.2 Obstacle Fields ............................... 46 3.3 Relocating Granular Patch that follows the vehicle . 48 3.4 Granular relocation algorithm ....................... 49 3.5 HMMWV navigating around obstacle, granular Patch does not collide with obstacles .................................. 51 3.6 Independent four granular relocating patches explored to improve simulation speeds, HMMWV chassis not visualized . 53 4.1 Experiment 1 Test results on Obstacle Field 1 . 56 4.2 Experiment 1 Test results on Obstacle Field 2 . 57 5.1 Terrain interactions on a single wheel on soft soil . 62 5.2 Comparison of Magic Formula Lateral Force Prediction to New Force Model 64 5.3 Effect of varying internal friction angle φ on lateral force prediction . 65 vi 5.4 Steering Sequence used for Open Loop Simulations . 67 5.5 Open Loop Trajectory of HMMWV over non-rotating granular terrains with different inter-particle friction coefficients µ . 68 5.6 Comparison of Trajectory Predicted by 2-DOF model using the Magic For- mula to estimate Tire Forces and the 2-DOF model using the new simplified force model ................................. 68 6.1 Experiment 2 Test results on Obstacle Field 1 . 71 6.2 Experiment 2 Test results on Obstacle Field 2 . 72 7.1 HMMWV unable to make forward progress in 6-DOF particle field . 82 9.2 Ray-Circle Intersection Visualization .................... 88 9.3 Visualization of Point in Polygon Algorithm Working Successfully . 91 1 1 INTRODUCTION Obstacle avoidance is a crucial capability for Autonomous Ground Vehicles (AGVs) of the future. This refers to a ground vehicle's ability to sense its surrounding environment, develop an optimal path around the obstacles in the environment, generate optimal control commands to satisfy that path, and physically navigate around the obstacles safely and to a desired endpoint. Safety is defined as avoiding collisions as well as enforcing limitations on excessive sideslip or tire lift-off. An ideal control algorithm is one that is capable of pushing a vehicle to its performance limits by using knowledge of its dynamic capabilities and surrounding environmental conditions, while still enforcing strict safety requirements. Although previous work has demonstrated use of Model Predictive Control (MPC) algorithms for obstacle avoidance on wheeled vehicles, more work is required to test the fidelity of these algorithms and determine where improvements are needed. One area in which MPC algorithms have yet to be tested is their ability to control a wheeled vehicle on granular terrain.